optical properties of 1999 ju3

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arXiv:1407.5569v1

[astro-ph.EP

]21Jul2014

Accepted on 2014 July 21 for publication in ApJ

Optical Properties of (162173) 1999 JU3:In Preparation for the JAXA Hayabusa 2 Sample Return Mission1

Masateru Ishiguro

Department of Physics and Astronomy, Seoul National University,

Gwanak, Seoul 151-742, South Korea

Daisuke Kuroda

Okayama Astrophysical Observatory, National Astronomical Observatory of Japan,

Asaguchi, Okayama 719-0232, Japan

Sunao Hasegawa

Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency,

Sagamihara, Kanagawa 252-5210, Japan

Myung-Jin Kim

Department of Astronomy, Yonsei University,

50 Yonsei-ro, Seodaemun-gu, Seoul 120-749, South Korea

Young-Jun Choi

Korea Astronomy and Space Science Institute,

776 Daedeokdae-ro, Yuseong-gu, Daejeon 305-348, South Korea

Nicholas Moskovitz

Lowell Observatory, 1400 W. Mars Hill Rd., Flagstaff, AZ 86001, USA

Shinsuke Abe

Department of Aerospace Engineering, Nihon University,

7-24-1 Narashinodai Funabashi, Chiba 274-8501, Japan

Kang-Sian Pan

Institute of Astronomy, National Central University,

300 Jhongda Road, Jhongli, Taoyuan 32001, Taiwan
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Jun Takahashi, Yuhei Takagi, Akira Arai

Nishi-Harima Astronomical Observatory, Center for Astronomy, University of Hyogo,

Sayo, Hyogo 679-5313, Japan

Noritaka Tokimasa

Sayo Town Office, 2611-1 Sayo, Sayo-cho, Sayo, Hyogo 679-5380, Japan

Henry H. Hsieh

Academia Sinica Institute of Astronomy and Astrophysics,

Roosevelt Rd., Taipei 10617, Taiwan

Joanna E. Thomas-Osip, David J. Osip

The Observatories of the Carnegie Institute of Washington, Las Campanas Observatory,

Colina El Pino, Casilla 601, La Serena, Chile

Masanao Abe, Makoto Yoshikawa

Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency,

Sagamihara, Kanagawa 252-5210, Japan

Seitaro Urakawa

Bisei Spaceguard Center, Japan Spaceguard Association,1716-3 Okura, Bisei-cho, Ibara, Okayama 714-1411, Japan

Hidekazu Hanayama

Ishigakijima Astronomical Observatory, National Astronomical Observatory of Japan,

1024-1 Arakawa, Ishigaki, Okinawa 907-0024, Japan

Tomohiko Sekiguchi

Department of Teacher Training, Hokkaido University of Education,

9 Hokumon, Asahikawa 070-8621, Japan

Kohei Wada, Takahiro Sumi

Department of Earth and Space Science, Graduate School of Science, Osaka University, 1-1

Machikaneyama, Toyonaka, Osaka 560-0043, Japan

Paul J. Tristram


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Mount John Observatory, P.O. Box 56, Lake Tekapo 8770, New Zealand

Kei Furusawa, Fumio Abe

Solar-Terrestrial Environment Laboratory, Nagoya University, Nagoya, 464-8601, Japan

Akihiko Fukui

Okayama Astrophysical Observatory, National Astronomical Observatory of Japan,

Asaguchi, Okayama 719-0232, Japan

Takahiro Nagayama

Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602, Japan

Dhanraj S. Warjurkar

Department of Physics and Astronomy, Seoul National University,

Gwanak, Seoul 151-742, South Korea

Arne Rau, Jochen Greiner, Patricia Schady, Fabian Knust

Max-Planck-Institut fur extraterrestrische Physik,

Giessenbachstrae, Postfach 1312, 85741, Garching, Germany

Fumihiko Usui

Department of Astronomy, Graduate School of Science, The University of Tokyo,

7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

Thomas G. Muller

Max-Planck-Institut fur extraterrestrische Physik,

Giessenbachstrae, Postfach 1312, 85741, Garching, Germany

ABSTRACT

Visiting Scientist, Institut de mecanique celeste et de calcul des ephemerides, Observatoire de Paris, 77

Avenue Denfert Rochereau, F-75014 Paris, France

Korea Astronomy and Space Science Institute, 776 Daedeokdae-ro, Yuseong-gu, Daejeon 305-348, South

Korea


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We investigated the magnitudephase relation of (162173) 1999 JU3, a target

asteroid for the JAXA Hayabusa 2 sample return mission. We initially employed

the international Astronomical UnionsHGformalism but found that it fits lesswell using a single set of parameters. To improve the inadequate fit, we em-

ployed two photometric functions, the Shevchenko and Hapke functions. With

the Shevchenko function, we found that the magnitudephase relation exhibits

linear behavior in a wide phase angle range (= 575) and shows weak nonlinear

opposition brightening at


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basis of optical and near-infrared spectroscopic observations (Binzel et al. 2001;Vilas 2008;

Lazzaro et al. 2013; Sugita et al. 2013; Pinilla-Alonso et al. 2013; Moskovitz et al. 2013).

Optical lightcurve observations indicated that JU3 is nearly spherical with an axis ratio of1.11.2 and a synodic rotational period of 7.625 0.003 h (Abe et al. 2008;Kim et al. 2013;Moskovitz et al. 2013). Mid-infrared photometry revealed that the asteroid has an effective

diameter of0.9 km (Hasegawa et al. 2008;Campins et al. 2009;Muller et al. 2011).Muller et al.(2014) recently constructed a sophisticated thermal model for JU3. They

determined an effective diameter of 87010 m as well as the possible pole orientation andthermal inertia. Motivated by their work, we thoroughly investigated the surface optical

properties of JU3 as part of the activity of the Hayabusa 2 project. This paper thus aims

to determine the geometric albedo, taking into account the updated effective diameter, and

characterize the optical properties useful for remote-sensing observations. In particular, we

emphasized the analysis of photometric data at low phase angles. In Section 2, we describe

the data acquisition and analysis. In Section 3, we employ three photometric models to fit

the magnitudephase relation. Finally, we discuss our results in Section 4 in terms of the

mission target of Hayabusa 2.

2. Data Acquisition and Analysis

2.1. Observations

Figure1shows the predicted V-band magnitudes and phase angles for given dates in

20072016 obtained by NASA/JPLs Horizons ephemeris generator2. The data set in 2007

2008 covers a large phase angle (up to 90), whereas that in 20112012 covers intermediate

to low phase angles (down to 0.3). The combined data thus provide a unique data set for

studying the magnitudephase relation of the C-type asteroid in a wide phase angle range in

which main-belt asteroids cannot be observed from earthbound orbit. A worldwide optical

observation campaign for JU3 was conducted in 20112012 not only to support the Hayabusa

2 project but also to explore the physical nature of the target asteroid. In particular, the

campaign gave considerable weight to acquiring the relative magnitudes for deriving the

rotational period and shape model (Kim et al. 2013; Kim 2014). Among the campaigndata, we selected magnitude data taken with calibration standard stars under good weather

conditions. In addition, we chose data with a substantial signal-to-noise ratio (i.e., S/N >

10) and/or data with even phase angle coverage. We also placed a priority on data at low

2http://ssd.jpl.nasa.gov/


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the image quality, but in principle, we set an aperture radius of about 23 times the full

width at half-maximum (FWHM), which is large enough to enclose the detected flux of

the asteroids and standard stars. The sky background was determined within a concentricannulus having projected inner and outer radii of3FWHM and4FWHM for pointobjects, respectively. Flux calibration was conducted using standard stars in the Landolt

catalog for the Johnson-Cousins B-, V-, RC-, and IC-band filters (Landolt 1992,2009); the

Sloan Digital Sky Survey (SDSS) catalog for the g -,r -, i-, andz-band filters (Ivezic et al.

2007); and the Two Micron All Sky Survey (2MASS) catalog for the J-, H-, and K-band

filters (Skrutskie et al. 2006). At Nishi-Harima Astronomical Observatory, the data were

taken under variable sky conditions, and the data taken with the Tenagra II and Magellan

II were obtained without taking standard star fields. To calibrate these data, we made a

follow-up observation of the same sky field with the UH2.2m and the same filter system.

2.3. Derivation of ReducedV Magnitude

As described above, our data were obtained with a variety of filters. To derive the

magnitudephase relation of JU3 using these data, we first examined the color relations

among the observed filter bands. The spectra of JU3 at 0.440.94 m has been studied well

and shows no rotational variability at the level of a few percent (Moskovitz et al. 2013). We

calculated the color indices using the spectrum in Abe et al. (2008), where they combined

optical and near-infrared spectra taken at the MMT Observatory and the NASAInfrared

Telescope Facility (see also Vilas 2008; Moskovitz et al. 2013). We considered that the

observed asteroid spectrum is a product of the asteroids reflectance and the solar spectrum,

and calculated the color indices (differences in magnitudes at two different bands) using the

following equation:

(mj mk) = 2.5log

rjrk

+ (mj mk) , (1)

where rj and rk are the reflectances at the effective wavelengths of the j-th and k-th band

filters, respectively, and (mj mk) is the color index of the sun between the j -th andk-thbands. We adopted the color indices of the sun and their uncertainties inHolmberg et al.

(2006). We used the formula inJordi et al.(2006) for converting from the Johnson-Cousins

BV RCIC system to the SDSS griz system. Table2 compares the observed and calculated

color indices. The observed color indices except for g-J(taken with GROND) were found

to match the calculated color indices to within the accuracy of our measurements (5%).We noticed that the g magnitude taken with GROND has an ambiguity in the calibration


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process due to unstable weather; it seems that the calculated g-J color index could be

more reliable than the observed one. Hereafter, we adopted the calculated color indices for

deriving the correspondingVmagnitude and tolerated the uncertainty of 5% associated withthe photometric system conversion in the following discussion.

In addition to the phase angle dependence, the observed magnitude of the asteroid

changed in time because of its rotation. For JU3, the rotational effect results in a magnitude

change no larger than0.1 mag with respect to the mean magnitude because it is nearlyspherical with an axis ratio of 1.11.2 (Kim et al. 2013). To determine the magnitudephase

relation, we corrected the rotational modulation and derived the magnitude averaged over

the rotational phase. If observations cover both the peak and the trough, we can derive

the mean magnitude as a representative value from a single-night observation. However,

because most of the data could not cover a substantial portion of the rotational phase, we

may mistake the mean magnitudes. Although the effect is not as large as a half-amplitude

of the lightcurve (i.e., 0.1 mag or less), we corrected the rotational effect in 2012 data by

deriving the zeroth-order term from the nightly data using an empirical Fourier model to

describe the relative magnitude change due to the rotation of JU3. It is given by the following

fourth-order Fourier series (Kim 2014):

(t) =

4h=1

[A2h1sin (2f h(tJD t0)) +A2hcos (2f h(tJD t0))] , (2)

where (t) denotes the relative magnitude change caused by the rotation of JU3, f= 3.1475

is the rotational frequency in day1, and tJD and t0 = 2456106.834045 (08:01:01.49 UT on

2012 June 28) are the observed median time in Julian days and offset time for phase zero

(see Figure 1 in Kim et al. 2013), respectively. A2h1 and A2h are constants given by A1= 0.0067, A2 = 0.030, A3 = 0.010, A4 = 0.055, A5 = 0.031, A6 = 0.019, A7 = 0.0070,

and A8 = 0.0033. Assuming the observed magnitudes are given by ( t) +HV(), we fitted

the observed magnitudes after color correction using Eq. (2) and derived the inferred mean

magnitudes, HV(). To evaluate how well the empirical lightcurve model reproduces the

observed lightcurve, we compared the model in Eq. (2) with lightcurve data taken at several

different nights in 2012; these include light curves taken on 2012 May 31 with MOA-cam3attached to MOA-II telescope at Mt. John Observatory, New Zealand (Sako et al. 2008;

Sumi et al. 2010), and on 2012 July 1719 with HCT. We found that the deviation is no

larger than a few percent. We considered a 4% uncertainty associated with the correction for

the lightcurve. Regarding 20072008 data, the lightcurve model may not applicable because

of the long interval of time betweentJD andt0. We adopted the observed mean magnitudes

and considered a 10% uncertainty.


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The observed corresponding V magnitude, HV(), was converted into the reduced V

magnitude HV(1, 1, ), a magnitude at a hypothetical position in the solar system, that is,

a heliocentric distance rh = 1 AU, an observers distance of = 1 AU, and a solar phaseangle , which is given by

HV(1, 1, ) = HV(rh, , ) 5 log(rh) . (3)

3. Results

In Figure2, we show the magnitudephase relation. It shows obvious phase darkening,

which is commonly observed in small solar system bodies. The photometric calibrationand color index correction appeared to work well, not only because our new data set is

smoothly connected to data fromKawakami (2009), but also because there is no systematic

displacement according to the observed filters. In the following subsections, we apply three

photometric functions to characterize the magnitudephase relation of JU3. For the fitting,

we employed the LevenbergMarquardt algorithm to iteratively adjust the parameters to

obtain the minimum value of2, which is defined as

2 = 1N

Nn=1

[HV(1, 1, )HV(1, 1, )]2 , (4)

whereHV(1, 1, ) is the reduced magnitude calculated by each model. N is the number ofmagnitude data points. The observed data points are weighted by HV(1, 1, )

2 for the

fitting, where HV(1, 1, ) denotes the error of reduced magnitude.

3.1. IAU HG formalism fitting

We initially applied theHG formalism described inLumme et al.(1984) andBowell et al.

(1989). The function was adopted by the International Astronomical Union (IAU) and has

been widely used as a standard asteroid phase curve. It has the mathematical form

HV(1, 1, ) = HV 2.5log

(1G)exp3.33tan0.63(/2)+G exp 1.87tan1.22(/2) , (5)


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where HV is the absolute magnitude in the V band, andG is the slope parameter indicative

of the steepness of the phase curve. By fitting the entire data set, we obtained values ofHV

= 19.12 0.03 and G =0.03 0.01 (dashed line in Figure 2). A careful examinationof the fitting results reveals that two-parameter fitting with the HG formalism cannot fitthe entire magnitudephase relation, causing a discrepancy in the absolute magnitude. The

fitting does not match the observational magnitude at small phase angles ( < 2). In

addition, the obtained slope parameterG takes a peculiar negative value, although asteroids

usually take positive values (Harris 1989). Because the HG formalism has been usually

applied for main-belt asteroids observed at 30, we fitted the data at < 30. We

obtained values ofHV = 19.22 0.02 and G = 0.13 0.02. We obtained the moderateGvalue this time, although the model is largely deviated from the observed data at >40.

3.2. Shevchenko function fitting

A simple but judicious model was proposed byShevchenko(1996) for approximating an

asteroids magnitudephase curves. It has the form

HV(1, 1, ) = C a

1 ++ b , (6)

where a is a parameter that characterizes the opposition effect amplitude, and b is a slope(mag deg1) describing the linear part of the phase dependence. C is given by C=HV+ a.

By fitting the entire data set, we obtained HV = 19.24 0.03, a = 0.19 0.04, and b =0.039 0.001 mag deg1. It is interesting to notice that the Shevchenko function fits theobserved data in a wide phase angle range from 0.3 to 75, although it was contrived to fit

observed data at small phase angles (i.e.


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a geometric albedo of 0.08 0.03. The albedo is in accordance with the geometric albedo ofJU3 (see below). The consistency of the phase slopes and the opposition effect amplitudes

between 10-km asteroids and sub-km asteroid JU3 may suggest that the magnitudephaserelation would be dominated by the albedo, not by the asteroid diameter. The amplitude

and width of the opposition effect are considered to represent the distance from the sun

theoretically (Deau 2012). The effect is caused by the apparent size of the sun when viewed

from asteroids. JU3 was observed at a solar distance ofrh = 1.36 AU, whereas the other

asteroids in Figure3were observed at rh = 1.83.4 AU. No significant difference is found

between JU3 and the other dark asteroids, most likely because the error is not small enough

to detect such a solar distance effect.

3.3. Hapke model fitting

Finally, we employed the Hapke model (Hapke 1981,1984,1986). It has been applied to

in-situ observational data taken with spacecraft onboard cameras. The Hapke model provides

an excellent approximation of the photometric function to correct for different illumination

conditions. However, because it has a complicated mathematical form with many parameters

(typically five or six), it often does not give a unique fit to the limited observational data

(Helfenstein & Veverka 1989;Belskaya & Shevchenko 2000). Some parameters are correlated

with others to compensate one another, so there are a number of best-fit parameter sets.

Despite this complexity, the application of the Hapke model is attractive in preparation for

in-situ observation by Hayabusa 2.

The observed corresponding V magnitudes are converted into the logarithm of I/F

(where F is the incidence solar irradiance divided by , and I is the intensity of reflected

light from the asteroid surface) as

2.5log

I

F

= HV(1, 1, )mV 5

2log

S

+mc , (7)

where mV is the V-band magnitude of the sun at 1 AU, Sis the geometrical cross sectionof JU3 in m2, and mc =5 log(1.4960 1011) =55.87 is a constant to adjust the lengthunit. We usedmV =26.74 (Allen 1973). We took the apparent cross section of JU3 S= (5.94 0.27) 105 m2, which is the equivalent area of a circle with a diameter of 870 10 m (Muller et al. 2014). The original Hapke model was contrived to characterize thebidirectional reflectance of airless bodies (Hapke 1981). However, the observed quantity in

this paper is the magnitude integrated over the sunlit hemisphere observable from ground-


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based observatories. We adopted the Hapke function integrating the intensity per unit area

over that portion of a spherical body (Hapke 1984). The equation is given as

I

F =

w8

[(1 +B()) P() 1] + r02

(1 r0)

1 sin

2

tan

2

ln

cot

4

+2

3r20

sin() + ( ) cos()

K(,) , (8)

where w is the single-particle scattering albedo. K(,) is a function that corrects for the

surface roughness parameterized by (Hapke 1984). The term r0 is given by

r0=11 w1 +

1 w . (9)

The opposition effect term B() is given by

B() = B0

1 + tan(/2)h

, (10)

where B0 characterizes the amplitude of the opposition effect, andh characterizes the width

of the opposition effect. We used the one-term HenyeyGreenstein single particle phase

function solution (Henyey & Greenstein 1941):

P() = (1 g2)

(1 + 2g cos() +g2)3/2 , (11)

where g is called the asymmetry factor. Positive values ofg indicate forward scatter, g=0

isotropic, and negative g backward scatter.For the fitting, we considered initial values in the possible ranges of the parameters, that

is, 0.01 w 0.09 at intervals of 0.02, 0.01 h 0.1 at intervals of 0.03, 0.5 g 0.1at intervals of 0.2, 0 B0 4.0 at intervals of 1, and 0 40 at intervals of 10, andconducted the parameter fitting. However, we soon realized that the fitting algorithm cannot

converge when these five parameters are variables. We found that, mathematically, the effect

of the surface roughness, , can be compensated by the other parameters to produce nearly


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identical disk-integrated curves; consequently, the fitting algorithm cannot converge. A

similar argument was made for Itokawas disk-integrated function, where it was claimed that

high phase angle data are necessary to constrain the surface roughness effect (Lederer et al.2008). We assumed to be 0, 10, 20, 30, or 40 and derived the other parameters for

the given values. The obtained Hapke parameters are summarized in Table 3 and the

magnitudephase relation with the parameters is shown in Figure 2and Figure4. In terms

of2, there is no significant difference between the models with different . However, our

magnitude data at high phase angles favour models with 30(see Figure4 at >70).

In Table 3, we calculated the Bond albedo (also known as the spherical albedo), AB,

which is the fraction of incident light scattered in all directions by the surface. It is given

byAB = qpV, where qis the value of the phase integral, defined as

q= 2

0

()

(0) sin() d . (12)

In comparison with the other mission target asteroids, JU3 has Hapke parameters sim-

ilar to those of the C-type asteroid Mathilde. We noticed that the resultant albedos are

independent of the surface roughness, although the other Hapke parameters depend on the

assumed roughness. The Hapke model matches well Shevchenkos model at the lowest phase

angle, yieldingHV= 19.24 0.03. From the absolute magnitude, we can conclude that JU3has a geometric albedo ofpV = 0.046 0.004. The derived albedo is consistent with thoseof C-type asteroids, that is, 0.0710.040 (Usui et al. 2013).

4. Discussion

4.1. Error Analysis

As we described above, we considered possible error sources with conservative estimates

and obtained the total error. Eventually, each corresponding V magnitude has a photo-

metric error of0.1 mag. The photometric models above fit the observed data within thephotometric errors, most likely because we may give adequate consideration to the errors.

As a result, each error in the magnitude data taken with a variety of filters and instruments

seems to be randomized, which provides a reliable absolute magnitude. We obtained a fit-

ting error of the absolute magnitude of 0.03 mag. It is important to note that the absolute

magnitude we derived differs greatly (0.4 mag) from that in the previous study ( Kawakami

2009), which was obtained on the basis of observation at >22 and is commonly referred
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to in previous research to derive the geometric albedo (Hasegawa et al. 2008;Campins et al.

2009;Muller et al. 2011). In general, the absolute magnitudes of main-belt asteroids have

been determined through ground-based observations at


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4.2. In Preparation for the Hayabusa 2 Mission

The primary goal of the Hayabusa 2 mission is to bring back samples from a C-type

asteroid or an asteroid analogous to C-type asteroids, following up on the Hayabusa 1 mission,

which returned a sample from the S-type asteroid Itokawa (Yoshikawa et al. 2008, 2012).

Because of the similarity of the spectra, C-type asteroids are considered to be parent bodies

of carbonaceous chondrite meteorites, which are abundant in organic materials and hydrous

minerals. In the nominal plan, multiple samplings are scheduled to obtain different types

of asteroid material on the basis of their composition and degrees of aqueous alteration and

space weathering. Because the reflectance at 0.55 m depends mainly on the abundance

of carbon compounds, the surface reflectance map will provide information useful for the

selection of the sampling sites. Therefore, speedy construction of the reflectance map is

crucial to the projects success. The observed reflectances at given wavelengths should beconverted to a standard geometry consisting of the incident angle i = 30 emission angle e

= 0, and phase angle = 30 using a photometric model. Among the models, the Hapke

model has been widely used to correct data taken with spacecraft onboard cameras (see,

e.g.,Clark et al. 1999,2002). Through this work, we have determined the Hapke parameters

except for the surface roughness. Because the disk-resolved reflectance is sensitive to the

surface roughness, we expect that it will be obtained uniquely once the JU3 images are taken.

We thus propose to determine the surface roughness while fixing the other four parameters on

a restricted basis by the magnitudephase relation. The construction of JU3s shape model

is essential to calculating the incident and emission angles. Once the shape is determined,

we expect that the full set of Hapke parameters will be fixed using the images taken withthe onboard cameras.

Our work provides useful information for the calibration of the onboard remote-sensing

devices such as the Optical Navigation Camera (ONC) and the Deployable CAMera (DCAM).

Specifically, we provide accurate magnitude models. Similar to the procedure on the Hayabusa

1 mission, measurements of JU3s lightcurve are planned for the purpose of flux calibration

(Sugita et al. 2013). A comparison of the magnitudephase relation in this paper and the

observed disk-integrated data count will enable the determination of the calibration fac-

tors, as we did using stellar observations during the cruising phase for Hayabusa Asteroid

Multi-band Imaging Camera (AMICA) (Ishiguro et al. 2010). Unlike the case of AMICA forHayabusa 1, we expect that the calibration parameters will be determined easily thanks to

the accurate photometric models in this paper.


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5. Summary

We examined the magnitudephase relation of (162173) 1999 JU3 using data taken from

ground-based observatories. The major findings of this paper are as follows:

1. The IAUHGformalism does not fit the observed data at small and large phase angles

( < 2 and >50) simultaneously using a single set of parameters. By fitting the

data set at


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This preprint was prepared with the AAS LATEX macros v5.2.


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19

20

21

22

23

0 10 20 30 40 50 60 70 80 90

CorrespondingVm

agnitude

Phase angle, (degree)

Magellan II (r'-band)IRSF (J-band)

Tenagra II (RC-band)GROND (JH-band)

UH88 (g'r'-band)Steward (RC-band)

Lulin (RC-band)Magellan I (RC-band)

Nayuta (RC-band)HCT (RC-band)Kawakami (2009) (RC-band)

H-G functionShevchenko function

Hapke function

19.0

19.2

19.4

19.6

19.8

20.00 2 4 6 8 10

Fig. 2. Magnitudephase relation of JU3. All observed magnitudes were converted into

corresponding V magnitudes assuming the color of the asteroid in Table2 at a hypothetical

position of 1 AU from the sun and observer. We show three models, that is, IAU H

G function with our best fit parameters, HV = 19.13 0.03 and G =0.006 0.012,Shevchenko function with the best fit parameters, a= 0.21 0.04, b = 0.039 0.001, andHV = 19.24

0.03, and Hapke model with one of the best fit parameter sets, = 20,

w= 0.041,g = 0.38, B0= 1.43, andh= 0.050.


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0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.01 0.1 1

Parameterforoppositioneffectamplitude,a

Geometric albedo, pV

Belskaya & Shevchenko (2000)Shevchenko et al. (2002)

Belskaya et al. (2003)Hasegawa et al. (2014)1999 JU3 (This work)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.01 0.1 1

Parameterforphaseslop

e,

b

Geometric albedo, pV

Belskaya & Shevchenko (2000)Shevchenko et al. (2002)

Belskaya et al. (2003)Hasegawa et al. (2014)

This work

Fig. 3. Geometric albedo dependences of parameters for the opposition effect ampli-

tude and linear phase slope in Shevchenkos function. The original data were obtained

fromBelskaya & Shevchenko (2000), Shevchenko et al. (2002), Belskaya et al. (2003), and

Hasegawa et al.(2014). We updated the albedo values using data in Usui et al.(2011).


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19

20

21

22

23

0 10 20 30 40 50 60 70 80 90

CorrespondingVmagnitude

Phase angle (degree)

Magellan II (r'-band)IRSF (J-band)

Tenagra II (RC-band)GROND (JH-band)

UH88 (g'r'-band)Steward (RC-band)Lulin (RC-band)

Magellan I (RC-band)Nayuta (RC-band)

HCT (RC-band)Kawakami (2009) (RC-band)

= 0 degree =10 degree =20 degree =30 degree =40 degree

Fig. 4. Comparison between five sets of Hapke model parameters in Table 3 ( =040

from top to bottom).


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Table 1. Observation Summary

Telescope Instrument Filter Date (UT)

This work

UH2.2ma Tek2048 r, g 2012 June 26, 27, July 12

IRSFb SIRIUS J, H, K 2012 May 30, 31, June 1, 2, 4

Magellan Ic IMACS RC 2012 April 57

Magellan IId LDSS3 g, r, i 2012 June 1

ESO/MPIe GROND g, r , i, z , J, H, K 2012 May 28, June 910

Tenagra IIf SITe 1k CCD RC 2012 May 31, June 79

Nayutag MINT RC 2012 June 22

HCTh HFOSC RC 2012 July 17

Stewardi Optical CCD V, RC 2007 September 1013

Lulinj EEV 1k CCD B, V, RC, IC 2007 July 1923, December 3, 78

2008 February 2728, April 2, 45

Kawakami (2009)

Kisok 2KCCD B, V, RC 2007 November 8

a The University of Hawaii 2.2-m Telescope, USA

b The InfraRed Survey Facility 1.4-m Telescope, South Africa

c Las Campanas Observatory Magellan I Baade Telescope, Chile

d Las Campanas Observatory Magellan II Clay Telescope, Chile

e La Silla Observatory ESO/MPI 2.2-m Telescope, Chile

f Tenagra II 0.81-m Telescope, USA

g The Nishi-Harima Astronomical Observatory Nayuta 2-m Telescope, Japan

h The Indian Institute of Astrophysics 2-m Himalayan Chandra Telescope, India

i Steward Observatory 61-in. (1.54-m) Kuiper Telescope, USA

j Lulin Observatory One-meter Telescope, Taiwan

k The University of Tokyo Kiso Observatory 1.05-m Schmidt Telescope, Japan


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Table 2: Color Indices

B-V V-RC V-IC g-r r-i V-J g-J

Observed(Kawakami 2009) 0.66 (0.06) 0.40 (0.06) 0.74 (0.07)

Observed (this work) 0.37 (0.03) 0.47 (0.03) 1.16 (0.05)

Calculated 0.65 (0.01) 0.34 (0.01) 0.72 (0.01) 0.45 (0.02) 0.13 (0.01) 1.21 (0.04) 1.48 (0.05)

Note. Numbers in the parentheses are errors of the color indices.


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Table 3. Hapke Parameters for JU3 and Other Mission Target Asteroids in V Band (550 nm)

Typea

wb

gc

d

(

) Be0 h

f

pg

V qh

AiB Reference

This work

1999 JU3 Cg 0.038 -0.39 [0] 1.52 0.049 0.045 0.32 0.014

0.039 -0.39 [10] 1.49 0.049 0.045 0.32 0.014

0.041 -0.38 [20] 1.43 0.050 0.045 0.31 0.014

0.046 -0.36 [30] 1.34 0.051 0.045 0.31 0.014

0.052 -0.34 [40] 1.21 0.051 0.044 0.30 0.013

Other mission targets

(253) Mathilde Cb 0.035 -0.25 19 3.18 0.074 0.041 0.33 0.013 Clark et a

(243) Ida S 0.22 -0.33 18 1.53 0.02 0.21 0.34 0.070 Helfenstein et a

(433) Eros S 0.43 36 1.0 0.022 0.29 0.39 0.12 Domingue et a

(951) Gaspra S 0.36 -0.18 29 1.63 0.06 0.22 0.49 0.11 Helfenstein et a

(25143) Itokawa Sk 0.70 40 0.02 0.141 0.19 0.11 0.021 Lederer et a

(5535) Annefrank S 0.63 -0.09 49 [1.32] 0.015 0.28 0.44 0.12 Hillier et a(4) Vesta V 0.51 -0.24 18 1.83 0.048 0.42 0.47 0.20 Li et al. (2013); Hasegawa et a

(2867) Steins E 0.66 -0.30 28 0.60 0.027 0.39 0.59 0.24 Spjuth et al.

Note. a Taxonomic type, b Single-scattering albedo, c Asymmetry factor, d Roughness parameter, e Opposition amplitude par

Opposition width parameter, g Geometric albedo, h Phase integral, and i Bond albedo. Parameters obtained at 630 nm.

Numbers in parentheses for are fixed values.

optical properties of 1999 ju3

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